10-1Y=10Y-1Y^2

Solution for 10-1Y=10Y-1Y^2 equation:

Simplifying
10 + -1Y = 10Y + -1Y2

Solving
10 + -1Y = 10Y + -1Y2

Solving for variable 'Y'.

Combine like terms: -1Y + -10Y = -11Y
10 + -11Y + Y2 = 10Y + -1Y2 + -10Y + Y2

Reorder the terms:
10 + -11Y + Y2 = 10Y + -10Y + -1Y2 + Y2

Combine like terms: 10Y + -10Y = 0
10 + -11Y + Y2 = 0 + -1Y2 + Y2
10 + -11Y + Y2 = -1Y2 + Y2

Combine like terms: -1Y2 + Y2 = 0
10 + -11Y + Y2 = 0

Factor a trinomial.
(1 + -1Y)(10 + -1Y) = 0

Subproblem 1
Set the factor '(1 + -1Y)' equal to zero and attempt to solve:

Simplifying
1 + -1Y = 0

Solving
1 + -1Y = 0

Move all terms containing Y to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1Y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1Y = 0 + -1
-1Y = 0 + -1

Combine like terms: 0 + -1 = -1
-1Y = -1

Divide each side by '-1'.
Y = 1

Simplifying
Y = 1
Subproblem 2
Set the factor '(10 + -1Y)' equal to zero and attempt to solve:

Simplifying
10 + -1Y = 0

Solving
10 + -1Y = 0

Move all terms containing Y to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1Y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1Y = 0 + -10
-1Y = 0 + -10

Combine like terms: 0 + -10 = -10
-1Y = -10

Divide each side by '-1'.
Y = 10

Simplifying
Y = 10
Solution
Y = {1, 10}